Solve the Problem B) C) D)

question 51

Multiple Choice

Solve the problem.
-At time t = 0 a particle is located at the point (4, -3, 2) . It travels in a straight line to the point (6, -2, 1) , has speed 2 at (4, -3, 2) and constant acceleration 6i - j - k. Find an equation for the position vector r(t) of the particle at time t.

• A) \(r ( t ) = \left( 3 t ^ { 2 } + \frac { 8 } { \sqrt { 29 } } t + 4 \right) i - \left( \frac { 1 } { 2 } t ^ { 2 } + \frac { 6 } { \sqrt { 29 } } t + 3 \right) j - \left( \frac { 1 } { 2 } t ^ { 2 } - \frac { 4 } { \sqrt { 29 } } t - 2 \right) k\)
• B) \(r ( t ) = \left( 3 t ^ { 2 } + \frac { 2 } { \sqrt { 6 } } t + 4 \right) i - \left( \frac { 1 } { 2 } t ^ { 2 } - \frac { 1 } { \sqrt { 6 } } t + 3 \right) j - \left( \frac { 1 } { 2 } t ^ { 2 } + \frac { 1 } { \sqrt { 6 } } t - 2 \right) k\)
• C) \(\mathbf { r } ( \mathrm { t } ) = \left( 3 \mathrm { t } ^ { 2 } + \frac { 4 } { \sqrt { 6 } } \mathrm { t } + 4 \right) \mathrm { i } - \left( \frac { 1 } { 2 } \mathrm { t } ^ { 2 } - \frac { 2 } { \sqrt { 6 } } \mathrm { t } + 3 \right) \mathrm { j } - \left( \frac { 1 } { 2 } \mathrm { t } ^ { 2 } + \frac { 2 } { \sqrt { 6 } } \mathrm { t } - 2 \right) \mathrm { k }\)
• D) \(\mathbf { r } ( \mathrm { t } ) = \left\{ 6 \mathrm { t } ^ { 2 } + \frac { 4 } { \sqrt { 6 } } \mathrm { t } + 4 \right) \mathrm { i } - \left( \mathrm { t } ^ { 2 } - \frac { 2 } { \sqrt { 6 } } \mathrm { t } + 3 \right) \mathrm { j } - \left( \mathrm { t } ^ { 2 } + \frac { 2 } { \sqrt { 6 } } \mathrm { t } - 2 \right) \mathbf { k }\)

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Definitions:

Personality

The unique combination of emotional, attitudinal, and behavioral response patterns of an individual.

Cattell

A reference to Raymond Cattell, a psychologist known for his work in personality theory, including the development of the 16 personality factor model.

Personality

The fusion of distinct traits that constitute a person's unique character.

Personality

The combination of characteristics or qualities that form an individual's distinctive character, influencing their behaviors, thoughts, and emotions.